Questions tagged [integer]
For challenges involving the manipulation of integers.
411
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RADD decomposition of an integer
Introduction
The \$RADD(n)\$ operation is defined as the sum of \$n + [\$ the number whose decimal representation are the decimal digits of \$n\$ in reverse order \$]\$, see A004086. After reversal, ...
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4
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Find a matrix whose sliding sum is the input
Given a matrix like this:
1 1 3 -2
3 -4 1 -1
1 1 1 0
0 -1 0 0
By taking a 2×2 "sliding sum", where the sum of every 2×2 region of the matrix is ...
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11
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Carryless factors
Carryless multiplication is an operation similar to binary long multiplication, but with XOR instead of addition:
...
- 18.4k
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Carry-less sum given a base b
Given a list of positive integers \$\mathcal I=I_1,I_2,I_3,...,I_n\$ and a base \$b>1\$ return their "carry-less sum", i.e. represent \$\mathcal I\$ in base \$b\$ and sum digit-by-digit ...
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Find number components with lowest distribution
Let us assume that we have number X.
Let us assume that we have positive integer "components" (C) of this ...
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Cryptic Multiplications
Given two non-negative integers e.g. 27, 96 their multiplication expression would be 27 x 96 = 2592.
If now each digits is ...
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Shifted auto-sum
Let’s take a positive integer such as 123. We define the shifted auto-sum of this integer as follows:
123 has 3 digits. We thus consider 3 copies of 123.
We stack ...
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6
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Exponential transform of an integer sequence
The exponential generating function (e.g.f.) of a sequence \$a_n\$ is defined as the formal power series \$f(x) = \sum_{n=0}^{\infty} \frac{a_n}{n!} x^n\$.
When \$a_0 = 0\$, we can apply the ...
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How far from binary?
Given a decimal integer n as input, output the smallest (in terms of absolute value) decimal integer m such that the absolute ...
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Find the nth Fibonacci number, where n is the mth Fibonacci number
Introduction
If \$\newcommand{\fib}{\operatorname{fib}}\fib(x)\$ calculates the \$x\$th Fibonacci number, write a program that calculates \$\fib(\fib(m))\$ for any integer value of \$m \ge 0\$. (Of ...
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Spell out an integer... in NDos' way
Objective
Given a positive integer, spell it out in the conlang I made.
Specification
Let \$n\$ be the inputted integer. \$n\$ shall be spelled out in the following specification. The entire spelling ...
- 4,295
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Is it 1089-able?
\$ 1089 \$ is a very special number. To prove why, select any 3-digit number whose first and last digits differ by at least 2. Then, reverse the digits, and take the difference of these two numbers. ...
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The interstice of two binary numbers
Given two integers, compute the two numbers that come from the blending the bits of the binary numbers of equal length(same number of digits, a number with less digits has zeros added), one after the ...
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Randomly Rounding
Input a decimal number and round it to an integer, randomly rounding up or down with a probability based on its fractional part, so the expected value of the output equals to the input value.
If ...
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Double bit rotation to the right [closed]
Given a positive integer as input, output that integer, but with its bits rotated two times to the right. Also, think of the number as a donut of bits, eg. ...
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3
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Line Islands in a Word Search
My third word search related challenge in a row. :)
Challenge:
Brief explanation of what a word search is:
In a word search you'll be given a grid of letters and a list of words. The idea is to cross ...
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3
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Find All Digitroot Cyclic Sequences With Length Greater Than One
Digital sum, DR, Digit root is the iterative process of summing digits of a number until you end up with a single digit root number: e.g. digit root of 12345 is 6 since 1 + 2 + 3 + 4 + 5 = 15 = 1+5. ...
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How-many-bonacci-like is this sequence?
Inspired by @emanresu A's Is it a fibonacci-like sequence? Make sure to upvote that challenge as well!
We say a sequence is Fibonacci-like, if, starting from the third term (\$1\$-indexed), each term ...
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10
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3
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Coordinates for a Heronian tetrahedron
Did you know that Heronian Tetrahedra Are Lattice Tetrahedra? A Heronian tetrahedron is a tetrahedron where
the length of each edge is an integer,
the area of each face is an integer, and
the volume ...
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28
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Sum of the first n elements of the sequence of 9's complement
Let's consider the following sequence:
$$9,8,7,6,5,4,3,2,1,0,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71...$$
This is the sequence of \$9\$'s complement of a number: that is, \$ a(x) = 10^...
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How many blocks make a "truncated square-pyramid garden"?
A truncated square-pyramid of height \$h\$ has \$h\$ square layers where each layer has a side \$1\$ greater than the one above it, apart from the top layer which is a square of blocks with a given ...
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Is it a fibonacci-like sequence?
The Fibonacci Sequence is a sequence of positive integers where the first two elements are 1 and the rest are the sum of the previous two. It begins \$1, 1, 2, 3, 5, 8, 13\$ and continues forever.
But ...
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Is given number a concat of two squares
Given a positive integer, determine if it can be represented as a concatenation of two square numbers. Concatenated numbers may not begin with 0 (except for 0). Any leading zeros in input should be ...
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27
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Prime a*b+c of N
Given an integer \$N\$, print or return integers \$a\$, \$b\$, and \$c\$ that satisfy all of the following conditions, if such integers exist:
\$a \times b + c = N\$
\$a\$, \$b\$, and \$c\$ are all ...
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6
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Represent any integer with an expression that uses no digit besides '4' [closed]
Fourward (Introduction)
I have an unhealthy obsession with the number 4. I love it so much, in fact, that seeing any other digit is frustrating to me. I therefour wish to create a 'Fourier ...
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Mirror an integer... in NDos' way
NDos' Numeral System
NDos' numeral system is a numeral system invented by me. It represents every nonnegative integer by a binary tree. Given a nonnegative integer \$n\$:
If \$n=0\$, it is ...
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15
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Encode integers with some others
Input a non-empty array of positive (greater than 0) integers. Output another non-empty array of positive integers which encode the input array. Output array does not use any numbers used in the input ...
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25
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Even sum subarrays
Given an array of integers, count the number of contiguous subarrays with an even sum. You may assume that the array is non-empty, and contains only non-negative integers.
This is code-golf, so the ...
- 20.3k
18
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6
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Is it an elementary matrix?
Consider a linear system of equations, in \$n\$ unknowns, expressed as
$$A \textbf x = \textbf b$$
where \$A \in M_{n,n}(\mathbb Z)\$ is an \$n \times n\$ matrix of integers, \$\textbf x\$ is a column ...
- 48.5k
13
votes
9
answers
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Bijective meets mixed base
Background
A bijective base \$b\$ numeration, where \$b\$ is a positive integer, is a bijective positional notation that makes use of \$b\$ symbols with associated values of \$1,2,\cdots,b\$.
...
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12
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2
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Branchless (MIPS) assembly code for median of 3
I was trying to write a short MIPS32 code for computing the median of three registers.
The rules:
Assume that some values are pre-loaded into $t0, ...
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12
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Nega-Zeckendorf representation
Background
Zeckendorf representation is a numeral system where each digit has the value of Fibonacci numbers (1, 2, 3, 5, 8, 13, ...) and no two consecutive digits can be 1.
Nega-Zeckendorf ...
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24
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18
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Double trace of a square matrix
Inspired by a question (now closed) at Stack Overflow.
Given a square matrix, let its double trace be defined as the sum of the entries from its main diagonal and its anti-diagonal. These are marked ...
- 102k
21
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9
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Self-referential triangle sequence
Output the flattened version of the sequence A297359, which starts like the following:
...
- 69.4k
29
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Swap Two Values in a List
Introduction:
Although we have a lot of challenges where swapping two items in a list is a subtask, like Single swaps of an array; Swap to Sort an Array; \$n\$ swaps into a nop; etc., we don't have ...
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16
votes
7
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Maybe fractal sequence?
Background
A fractal sequence (Wikipedia; MathWorld) is an infinite sequence of positive integers meeting the following conditions:
Each positive integer appears infinitely many times in the sequence....
- 69.4k
20
votes
12
answers
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Minimally prepend numbers to get a symmetric Young diagram
Background
A Young diagram is a diagram that represents a nonincreasing sequence of positive integers using left-justified rows of squares. As an example, 5, 4, 1 ...
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24
votes
31
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"-rot" transform
Background
-rot transform (read as "minus-rot transform") is a sequence transformation I just invented. This transform is done by viewing the sequence as a stack in Forth or Factor (first ...
- 69.4k
12
votes
8
answers
1k
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Boustrophedon transform
Related: Boustrophedonise, Output the Euler Numbers (Maybe a new golfing opportunity?)
Background
Boustrophedon transform (OEIS Wiki) is a kind of transformation on integer sequences. Given a sequence ...
- 69.4k
18
votes
4
answers
625
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Calculate the integer square root of a matrix
Let \$A\$ be a square matrix that is at least \$2 \times 2\$ where each element is an integer. \$A^2 = A \times A\$ will then have the same dimensions as \$A\$, and will have integer elements. For ...
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5
votes
5
answers
232
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Potential nonzero entries in an irregular sequence
Background
A338268 is a sequence related to a challenge by Peter Kagey. It defines a two-parameter function \$T(n,k)\$, which counts the number of integer sequences \$b_1, \cdots, b_t\$ where \$b_1 + \...
- 69.4k
16
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19
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Compare positions of integers in this sequence
A001057 is one way to represent an integer as a natural number. It lists them according to the following pattern:
0, 1, -1, 2, -2, 3, -3, 4, -4, ...
In this ...
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15
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27
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Make an array of random 128 bit integers
Given an input value \$n\$, construct an array of \$n\$ random 128 bit (unsigned) integers. The integers should be uniformly random.
Your code can use any in built random number generation function ...
user7467
8
votes
4
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Hexagonal section numbers
Introduction
Let's draw some regular hexagons formed by hexagonal tiles, marking the vertices of the tiles with dots. Then we will count the number of dots.
...
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22
votes
22
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Longest Zero Sum Sub-array
Given an array of integers. Find out its longest sub-array (contiguous subsequence) whose sum is 0.
The sub-array for output may be an empty array.
Input
Input an array of integers.
Output
Output the ...
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5
votes
3
answers
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Is this an ordinal transform? [duplicate]
Related: What's my telephone number? which asks to calculate the terms of A000085, the number of possible ordinal transforms of length n.
Background
Ordinal transform is a transformation on an integer ...
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39
votes
15
answers
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Maximum number of squares touched by a line segment
Consider a square grid on the plane, with unit spacing. A line segment of integer length \$L\$ is dropped at an arbitrary position with arbitrary orientation. The segment is said to "touch" ...
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votes
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Is this a Permutation of 1..n
Input a non-empty array with \$n\$ positive integers. Test if the input array contains every integer in \$1\cdots n\$.
In case you prefer 0-indexed numbers, you may choose to input an array of non-...
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Give me odd, even, square, cube, prime and composite 3-digit numbers
Given a string which is guaranteed to be either odd, even, square, ...
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